In recent years, researchers in artificial intelligence have become interested in replicating human physical reasoning talents in computers. One of the most important skills in this area is the ability to predict how physical systems behave. This thesis discusses an implemented program that can generate algebraic descriptions of how systems of rigid bodies evolve over time. Discussion about the design of this program identifies a powerful physical reasoning paradigm and knowledge representation approach based on mathematical model construction and algebraic reasoning. This paradigm offers a number of advantages over methods that have become popular in the field, and seems a promising approach for reasoning about a wide variety of classical mechanics problems.